Re: Zero/Dope and Magnification changes.
If it's a decent scope, the zero shouldn't change no matter what the magnification.
some less than acceptable quality scopes seem to "drift" when the magnification is changed.
alot of that to is not adjusting the parallax properly, giving the impression that the zero has drifted when the magnification is changed.
as i mostly run mildots, usually i'll do all my preliminary zeroes on 10x, to give me the same sight picture & ranging info.
i think it's also important to set a zero on a particular rifle for the distance and magnification that the rifle will mostly be used at, so the sight picture remains the same.
example: my savage mkii is zeroed at 25 yds (10X) as i use it for short range target, short range squirrel hunting. if i do crank up the power at a day at the range, no drift in the zero is experienced.
my .22 mag (10x) zero is 50yds, with it being my turkey / walkaround rifle, i feel it's a good intermediate distance and the flatter trajectory means i really don't have to do much adjusting till 30 yards shorter or 30 yards longer.
my cz455 .22lr has a 100Y zero as that's where i "begin" with that rifle.
my silhouette setup i have a 40 Meter zero as that's the distance of the first target, then i "crank turrets" accordingly throughout the next 3 target distances. here i'll start on 6X, next target 60Meters i'll move it to 10X, next target 77 meters is 12X, and the last target 109 Meters is 12X. to me, the target appears to be the same size in the sight picture, lending less mind games to feeling pressure on the smaller but closer targets, or the larger but further targets.
neither one of those optics suffer from a "drift" in the zero whether i set it on 6X, 24x, or 32X, unless of course the parallax isn't adjusted properly. again, the zero shouldn't change if the power is adjusted. if your optic is doing that after ruling out parallax adjustment, it's either get a different scope, or drive yourself crazy chasing a zero everytime you turn the magnification ring.
With the OP's example of the FFP, the only thing that should change is the POI with the holdover marks (if any) on the reticle when the power is adjusted.
sorry for the long winded answer.